Question

Katrina wants to estimate the proportion of adultAmericans who read at least 10 books last year. To do so, she obtains a simple random sample of 100 adult Americans and constructs a 95% conﬁdence interval. Matthew also wants to estimate the proportion of adult Americans who read atleast 10 books last year. He obtains a simple random sample of 400 adult Americans and constructs a 99% conﬁdence interval.Assuming both Katrina and Matthew obtained the same point estimate, whose estimate will have the smaller margin of error? Justify your answer.